On q-functional equations and excursion moments

Richard C (2009)

Publication Type: Journal article

Publication year: 2009

Journal

Discrete Mathematics Elsevier

Publisher: Elsevier

Book Volume: 309

Pages Range: 207--230

Journal Issue: 1

DOI: 10.1016/j.disc.2007.12.072

Abstract

We analyse q $q$ -functional equations arising from tree-like combinatorial structures, which are counted by size, internal path length, and certain generalisations thereof. The corresponding counting parameters are labelled by a positive integer k $k$ . We show the existence of a joint limit distribution for these parameters in the limit of infinite size, if the size generating function has a square root as dominant singularity. The limit distribution coincides with that of integrals of k $k$ th powers of the standard Brownian excursion. Our approach yields a recursion for the moments of the limit distribution. It can be used to analyse asymptotic expansions of the moments, and it admits an extension to other types of singularity.

Authors with CRIS profile

Christoph Richard Lehrstuhl für Mathematische Stochastik

How to cite

APA:

Richard, C. (2009). On q-functional equations and excursion moments. Discrete Mathematics, 309(1), 207--230. https://doi.org/10.1016/j.disc.2007.12.072

MLA:

Richard, Christoph. "On q-functional equations and excursion moments." Discrete Mathematics 309.1 (2009): 207--230.

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